A scenic overlook which extends over a ravin is shaped like a kite. I’m slow help

What is the constant for this direct variation when x=2 and y=6

NemiM [27]

The constant of variation = 3

8 0

3 years ago

Out of 16 spins, a purple-and-red spinner landed on purple 9 times and on red 7 times. Based on experimental probability, how ma

Diano4ka-milaya [45]

Answer:

Option A.

Step-by-step explanation:

It is given that out of 16 spins, a purple-and-red spinner landed on purple 9 times and on red 7 times..

Experimental probabilities are

$P(Purple)=\dfrac{Purple}{Total}=\dfrac{9}{16}$

$P(Red)=\dfrac{Red}{Total}=\dfrac{7}{16}$

Based on experimental probability, we need to find how many of the next 64 spins would we expect on land on red.

The expected number of red in 64 spins is

$\text{Expected red}=64\times P(Red)$

$\text{Expected red}=64\times \dfrac{7}{16}$

$\text{Expected red}=28$

Therefore, the correct option is A.

7 0

3 years ago

Let M be the closed surface that consists of the hemisphere

ycow [4]

Since $M$ is closed, you can use the divergence theorem: The flux of $\vec E(x,y,z)$ across $M$ is

$\displaystyle\iint_{\partial M}\vec E\cdot\mathrm d\vec S=\iiint_M(\nabla\cdot\vec E)\,\mathrm dV=54\iiint_M\mathrm dV$

which is 54 times the volume of the hemisphere centered at (0, 0, 0) with radius 1, $\boxed{36\pi}$ .

Judging by the question content, you're supposed to find this value by computing the the integral of $\vec E$ across $M_1$ and $M_2$ .

Across $M_1$ :

Parameterize the hemisphere by

$\vec r(u,v)=(\cos u\sin v,\sin u\sin v,\cos v)$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ . Take the normal vector to $M_1$ to be

$\dfrac{\partial\vec r}{\partial v}\times\dfrac{\partial\vec r}{\partial u}=(\cos u\sin^2v,\sin u\sin^2v,\sin v\cos v)$

The flux of $\vec E$ across $M_1$ is

$\displaystyle\iint_{M_1}\vec E\cdot\mathrm d\vec S=18\int_0^{\pi/2}\int_0^{2\pi}(\cos u\sin v,\sin u\sin v,\cos v)\cdot\left(\dfrac{\partial\vec r}{\partial v}\times\dfrac{\partial\vec r}{\partial u}\right)\,\mathrm du\,\mathrm dv$

$=\displaystyle18\int_0^{\pi/2}\int_0^{2\pi}\sin v\,\mathrm du\,\mathrm dv=36\pi$

Across $M_2$ :

Parameterize the disk by

$\vec s(u,v)=(u\cos v,u\sin v,0)$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal to $M_2$ to be

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec u}{\partial v}=(0,0,-u)$

Then the flux across $M_2$ is

$\displaystyle\iint_{M_2}\vec E\cdot\mathrm d\vec S=18\int_0^{2\pi}\int_0^1(u\cos v,u\sin v,0)\cdot\left(\frac{\partial\vec s}{\partial v}\times\frac{\partial\vec s}{\partial u}\right)\,\mathrm du\,\mathrm dv=0$